I have 2 kinds of questions relating to quadratic equation to ask.
Firstly,
find the range of values of a for which ax^2 - 8x + a >6
for such questions, it is like those ax^2 +bx + c >0, so discriminant is ALWAYS less than zero.
for the second type of question, find the set of x for which x^2 + 2 >/= (2x+1)(x-2)...
the discriminant for such an equation, do we FOLLOW the sign left after we have manipulated the equation?
Originally posted by anpanman:I have 2 kinds of questions relating to quadratic equation to ask.
Firstly,
find the range of values of a for which ax^2 - 8x + a >6
for such questions, it is like those ax^2 +bx + c >0, so discriminant is ALWAYS less than zero.
for the second type of question, find the set of x for which x^2 + 2 >/= (2x+1)(x-2)...
the discriminant for such an equation, do we FOLLOW the sign left after we have manipulated the equation?
Hi,
You are right for the first type :)
The second type of question is an inequality involving a quadratic expression, which is to be solved. The usual approach is to factorise or use the formula or completion of a square (when the expression cannot be factorised directly). In the example that you gave, we'll have steps that'll simplify to
x^2 - 3x - 4 <= 0,
then we'll factorise to obtain
(x + 1)(x - 4) <= 0,
from which we arrive at
-1 <= x <= 4
as our final answer.
Thanks!
Cheers,
Wen Shih